Recognition of tractable DNFs representable by a constant number of intervals
| Autor: | Ondřej Čepek, Radek Hušek |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Product term Parity function Applied Mathematics Boolean circuit Two-element Boolean algebra 0102 computer and information sciences 02 engineering and technology 01 natural sciences Theoretical Computer Science Combinatorics Computational Theory and Mathematics 010201 computation theory & mathematics Maximum satisfiability problem 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Boolean expression Boolean satisfiability problem Boolean function Mathematics |
| Zdroj: | Discrete Optimization. 23:1-19 |
| ISSN: | 1572-5286 |
| DOI: | 10.1016/j.disopt.2016.11.002 |
| Popis: | In this paper we focus on a less common way how to represent Boolean functions, namely on representations by intervals of truepoints and by switch-lists. There are two problems connected to such representation: (1) a knowledge compilation problem, i. e. a problem of transforming a given representation of a Boolean function (Boolean formula, binary decision diagram, Boolean circuit, …) into an interval or switch-list representation, and (2) a knowledge compression problem, i. e. a problem of finding the most compact interval or switch-list representation among those which represent the given function. We will summarize known results about these two problems and present generalizations in both areas. The main result is a polynomial time algorithm that for a Boolean function given by a tractable formula outputs a shortest interval and switch-list representations provided that the number of switches (intervals) is bounded by a constant. This algorithm can be also thought of as a polynomial time recognition algorithm for the class of k -switch (or k -interval) functions given by a tractable formula for any fixed k . |
| Databáze: | OpenAIRE |
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